The previous construction of ZAPs [Dwork and Naor, FOCS 00] was based on trapdoor permutations. The two previous NIWI constructions were based either on ZAPs and a derandomization-type complexity assumption [Barak, Ong, and Vadhan CRYPTO 03], or on a specific number theoretic assumption in bilinear groups [Groth, Sahai, and Ostrovsky, CRYPTO 06].

The Discrete Logarithm Problem is at the base of the famous Diffie Hellman key agreement algorithm and many others. The key idea behind Diffie Helmann is the usage of the Discrete Logarithm function in (Z/pZ)∗ as a trap door function. The Discrete Logarithm function output in (Z/pZ)∗ seems to escape to any attempt of finding some sort of pattern. Nevertheless some new characterization will be introduced together with a novel and more efficient trial multi- plication algorithm.

Camellia is one of the widely used block ciphers, which has been selected as an international standard by ISO/IEC. In this paper, we focus on the key-recovery attacks on reduced-round Camellia-192/256 with meet-in-the-middle methods. We utilize multiset and the differential enumeration methods which are popular to analyse AES in the recent to attack Camellia-192/256. We propose a 7-round property for Camellia-192, and achieve a 12-round attack with $2^{180}$ encryptions, $2^{113}$ chosen plaintexts and $2^{130}$ 128-bit memories. Furthermore, we present an 8-round property for Camellia-256, and apply it to break the 13-round Camellia-256 with $2^{232.7}$ encryptions, $2^{113}$ chosen ciphertexts and $2^{227}$ 128-bit memories.

Description: This thesis aims at defining software-level countermeasures against fault attacks on an up-to-date microcontroller. To perform such an analysis, this thesis relies on a hardware-level attacker's fault model. This fault model is obtained by using an electromagnetic fault injection experimental process.[...]

A sensor network is a network comprised of many small, wireless, resource-limited nodes that sense data about their environment and report readings to a base station. One technique to conserve power in a sensor network is to aggregate sensor readings hop-by-hop as they travel towards a base station, thereby reducing the total number of messages required to collect each sensor reading. In an adversarial setting, the ability of a malicious node to alter this aggregate total must be limited. We present three aggregation protocols inspired by three natural key pre-distribution schemes for linear networks. Assuming no more than k consecutive nodes are malicious, each of these protocols limits the capability of a malicious node to altering the aggregate total by at most a single valid sensor reading. Additionally, our protocols are able to detect malicious behavior as it occurs, allowing the protocol to be aborted early, thereby conserving energy in the remaining nodes. A rigorous proof of security is also given for each protocol.

Recent developments in Multi-party Computation (MPC) has resulted in very efficient protocols for dishonest majority in the preprocessing model. In particular, two very promising protocols for Boolean circuits have been proposed by Nielsen et al. (nicknamed TinyOT) and by Damg ̊ard and Zakarias (nicknamed MiniMac). While TinyOT has already been implemented, we present in this paper the first implementation of MiniMac, using the same platform as the existing TinyOT implementation. We also suggest several improvements of MiniMac, both on the protocol design and implementation level. In particular, we suggest a modification of MiniMac that achieves increased parallelism at no extra communication cost. This gives an asymptotic improvement of the original protocol as well as an 8-fold speed-up of our implementation. We compare the resulting protocol to TinyOT for the case of secure computation in parallel of a large number of AES encryptions and find that it performs better than results reported so far on TinyOT, on the same hardware.

We study the Reliable Broadcast problem in incomplete networks, under the locally bounded adversarial model (Koo, 2004), that is, there is a known bound on the number of players that a Byzantine adversary controls in each player\'s neighborhood. We generalize the model

to the more realistic non-uniform case, by allowing this bound to vary from node to node.

We first settle an open question of Pelc and Peleg (2005) in the affirmative, by showing that Koo\'s Certified Propagation Algorithm (CPA) for ad hoc networks is indeed unique, that is, it can tolerate as many local corruptions as any other non-faulty algorithm, thus having optimal resilience. Actually, we prove the stronger result that a natural extension of CPA is unique for the non-uniform model. We do this by providing a necessary and sufficient condition for reliable broadcast in ad hoc networks. On the other hand, we show that it is NP-hard to check whether this condition holds for a given graph G.

We also study known topology networks and prove that a topological condition, shown by Pelc and Peleg to be necessary for the existence of a Broadcast algorithm, is also sufficient. This leads to an optimal resilience algorithm for known networks as well. On the downside, we prove that PPA is inefficient. However, we are able to provide evidence showing that probably no efficient protocol of optimal resilience exists.

We take one more step, by considering a hybrid between ad hoc and known topology networks: each node knows a part of the network, namely a connected subgraph containing itself. We show that this partial knowledge model allows for more accurate reliable broadcast

algorithms.

Finally, we show that our results extend to the general adversary model. This, among others, means that an appropriate adaptation of CPA is unique against general adversaries in ad hoc networks.